Ply (game theory)

{{Short description|Game theory term}}

In two-or-more-player sequential games, a ply is one turn taken by one of the players. The word is used to clarify what is meant when one might otherwise say "turn".

The word "turn" can be a problem since it means different things in different traditions. For example, in standard chess terminology, one move consists of a turn by each player; therefore a ply in chess is a half-move. Thus, after 20 moves in a chess game, 40 plies have been completed—20 by white and 20 by black. In the game of Go, by contrast, a ply is the normal unit of counting moves; so for example to say that a game is 250 moves long is to imply 250 plies.

In poker with n players the word "street" is used for a full betting round consisting of n plies; each dealt card may sometimes also be called a "street". For instance, in heads up Texas hold'em, a street consists of 2 plies, with possible plays being check/raise/call/fold: the first by the player at the big blind, and the second by the dealer, who posts the small blind; and there are 4 streets: preflop, flop, turn, river (the latter 3 corresponding to community cards). The terms "half-street" and "half-street game" are sometimes used to describe, respectively, a single bet in a heads up game, and a simplified heads up poker game where only a single player bets.[https://pokerbooks.lt/books/en/The%20Mathematics%20of%20Poker.pdf Chen, Bill and Ankenman, Jerrod. The Mathematics of Poker], p110

The word "ply" used as a synonym for "layer" goes back to the 15th century.[http://www.etymonline.com/index.php?term=ply Online Etymology Dictionary, "ply"] (cited 24 April 2011) Arthur Samuel first used the term in its game-theoretic sense in his seminal paper on machine learning in checkers in 1959,[https://researcher.ibm.com/researcher/files/us-beygel/samuel-checkers.pdf A.L. Samuel, March 3, 1959: Some Studies in Machine Learning Using the Game of Checkers] (cited 25 August 2006) but with a slightly different meaning: the "ply", in Samuel's terminology, is actually the depth of analysis ("Certain expressions were introduced which we will find useful. These are: Ply, defined as the number of moves ahead, where a ply of two consists of one proposed move by the machine and one anticipated reply by the opponent"[https://researcher.ibm.com/researcher/files/us-beygel/samuel-checkers.pdf A.L. Samuel, March 3, 1959: Some Studies in Machine Learning Using the Game of Checkers], p. 601 (cited 2 May 2018)).

In computing, the concept of a ply is important because one ply corresponds to one level of the game tree. The Deep Blue chess computer which defeated Kasparov in 1997 would typically search to a depth of between six and sixteen plies to a maximum of forty plies in some situations.{{cite journal | url=https://www.sciencedirect.com/science/article/pii/S0004370201001291 | doi=10.1016/S0004-3702(01)00129-1 | title=Deep Blue | year=2002 | last1=Campbell | first1=Murray | last2=Hoane | first2=A.Joseph | last3=Hsu | first3=Feng-Hsiung | journal=Artificial Intelligence | volume=134 | issue=1–2 | pages=57–83 | s2cid=662187 | url-access=subscription }}